
S9^ 




LIBRARY OF CONGRESS. 

Cliap..:..._._. Copyright No.. 



Shelf. 



xS-H 



UNITED STATES QF AMERICA. 



n 



ECLECTIC SYSTEM OF INDUSTRIAL DRAWING 



ELEMENTS of PERSPECTIVE 



BY 



CHRISTINE GORDON SULLIVAN, A.M., Ph.D. 

Supervisor of Art Education in the Cincinnati Public Schools 

Author of Eclectic System of Drawings Class Book for High Schools^ Manual for Normal 

Schools and Teachers, Projections and Elements of Mechanical Drawing 




NEW YORK •:• CINCINNATI •:• CHICAGO 

AMERICAN BOOK COMPANY 







14398 



Copyright, 1898, by 
American Book Company 



8UL. eLE. PER*. 

5. P. 1 




Twti v.urito BcCtiVED. 



2nJ 



189C3. 




ELEMENTS OF PERSPECTIVE. 



CHAPTER I. 



PerspECTivk is the art of representing objects as they appear 
and not as they really are.' 

A perspective drawing is one in which we have the relative 
heights and distances of different parts according to the angles and 
distances at which they stand in reference to the observer. If the 
student understands the principles by which a square or cube is 
correctly placed in perspective, he can, with little difficulty, make 
a representation of more complicated objects in their true pro- 
portions. 

(3) 



EI.BMENTS AND Rules of Perspective. 



Certain lines are supposed to exist by which we determine the 
direction of the lines in the object to be drawn ; each one of these 
lines occupies a certain position with regard to the observer, and 
also with regard to the picture plane, and they are governed by 
rules, deduced from the sciences of Optics and Geometry. Before 
giving any of these rules, it will be necessary to define terms with 
which the student must become familiar — picture plane, ground 
plane, horizon, base, etc. The most important of these is the term 
picture plaiie or plane of delineation (page 12). The position of 
this plane with regard to the object to be represented determines 
whether the drawing is to be made in parallel, angular, or oblique 
perspective (page 11). 

The picture plane or plane of delineation is an imaginary plane 
parallel to the observer and perpendicular to 'the ground plane. 
The rays proceeding from an object (visual rays) pass through this 
plane. 





Fi^. 2. 



The visual angle is the angle formed by drawing lines from 
the extremities of any line to the eye ; the angle varies with the 
size and distance of an object. 

The visual angles are formed by lines extending .from a and b 
to the eye. 

If these rays proceed from a rectangular surface they form a 
pyramid of rays (Fig. 3), the vertex in the eye of the observer. If 
the rays proceed from a round surface, they form a cone of rays 
(Fig- 4). 



Elements and Rules of Perspective. 





Fig' 3- 



t^g. 4. 



The base from which the rays proceed is termed the ^e/d of 
view. The distance cd, in Fig. 4, represents the cross diameter of 
the field of view. Lines drawn from these points to the eye form 
an angle of 60° (one-sixth of a circle). When looking at a point 
one can not see more than is included in an angle of 60°, and not 
more than one-half of this (30°) distinctly. 



CHAPTER II. 

The apparent size of an object varies. according to the distance 
at which it is situated from the eye of the observer. The size of an 
object appears to diminish as it recedes from the eye; an object at a 
distance of thirty feet from the observer appears one-half as large 
as the same object at a distance of fifteen feet from the observer. At 
a distance of one hundred feet, it will appear one- fourth as large as 
it will at a distance of twenty-five feet from the observer. 



^^^^"^ 


a 




c 


.^^^===^^^^^^^ — '■ 




1 1 1 1 1 1 1 — 


- 


\^^^^^J^^^ 15 


ft. 


30 


n. 








- 




b 




d 



mg. 5. 



Figure 5 represents the Hue 8 feet long at a distance of 15 feet, and the 
same line again at a distance of 30 feet. At a distance of 30 feet, it appears 
one-half the length of the line at a distance of 15 feet. 



If an object is at R. A. to the Hne of direction, (a Hne that 
extends from the eye of the observer to the object,) no matter how 
far removed from the eye, the apparent shape remains the same, the 
size only varies. A cube viewed in this position would be repre- 
sented on a plane surface by a square, and a rectangular box by a 

(6) 



Elements and Rules of Perspective. 



rectangle, whether viewed at a distance of 5 feet or at a distance of 
50 feet. 

Fig. 6 represents the appearance of a cube when the line of direction is 
perpendicular to the point a. 
Fig. 7 represents the ap- 
pearance of a box when the 
line of direction is perpen- 
dicular to the point b. 





Tig. 6. 



r^g. 7. 



If an object is viewed at an angle, the apparent shape then 
varies. If we take a square figure and view it at a distance of 20 
feet, the line of direction at right angles with the plane of the figure, 
the apparent shape is a square^ and will be a square as long as it is 
viewed in that position. But let it occupy any position save that in 
which it is at right angles to the line of direction, and it will no 
longer appear of a square form. It will, if transferred to a flat 
surface, be represented by a figure that is not square. 

As long as the square is parallel to the observer the opposite 
parallel lines do not appear to meet, but if we turn the square so that 
the right side is at a greater distance from the observer than the left 
side, then the upper and lower lines of the square, though parallel 
in reality, appear to approach. If a picture were made of it on 
paper, in this position, we should have the two vertical lines of the 
square, those that are not at an angle with, but parallel to the 
obser^^er, represented by vertical lines. The line representing the 
right side, of course, is shorter than the line representing the left 
side, because it is farther from the observer ; but those lines that are 
at an angle with the plane of delineation or picture plane (this is an 
imaginary plane between the observer and the object) are not rep- 
resented as they are, but are represented in the drawing by two 



8 



Elements and Rules of Perspective. 




Fig. 8, 




Fig. 9. 



lines that will, if suflficiently 
prolonged, meet in a point. 

Fig. 8 represents a square adcd in 
perspective, the side dc at a greater 
distance from the observer than the 
side ad, and the lines ad and dc 
(parallel in reality) tending toward 
the point P. 

If the square is de/ow the 
level of the eye, the sides that 
recede from the observer tend 
to a point above the square. 

Fig, 9 represents a square below 
the level of the eye, which is here 
denoted by the horizontal line. 
In this the lines dc and ab at an angle to the observer, recede toward 
and appear to meet in the point P. 

If the square is above the 

level of the eye, the lines that 

recede from the observer tend 

to a point below the square. 

Fig. lo represents a square in 
perspective above the level of the 
eye. The lines ad and dc, that are 
at an angle with the picture plane, 
recede and meet in the point P. 

In Fig. II a very large square is 
represented, resting on the plane 
on which the observer stands, and 
extending above his head. The 
lines dc and ad that are at angles 
to the plane meet, if produced, in 
the point P. The line dc above 




Fig. lo. 




Fig, J J. 



Elements and Rules of Perspective. 



the level of the eye tends down to the point P, and the line ab below 
the level of the eye tends up to the same point. 

The point to which these receding lines recede, tend, or vanish, 
is called a vanishing point ; it is on a level line, vSituated opposite 
the eye of the observer. In this 
case the vanishing point is on 
the right of the squares. 

If these squares were so placed 
that the left side was farther 
from the observer than the right 
side, then the receding lines 
would vanish to a point on the 
left of the squares. 



In Figs. 12 and 13 the vanishing 
points for the squares are on the left. 




Fig. 13. 



In representing a solid, such as a cube, if the front face is 
parallel to the obser^T-er, the receding lines vanish in one point 
(Fig. 14). If the cube is at an angle to the obsen^er, then instead 
of one vanishing point there are two, — one on each side of the 
object (Fig. 15). 




Jp^g. 14- 

Fig. 14 represents a view of a 
cube parallel to the observer. 



Pig. X5. 

Fig. 15 represents a view of a cube 
at an angle to the observer. 



The illustrations thus far show the direction of the lines when 



lO 



E1.KMKNTS AND RUI.KS OF Perspective. 



the objects are at right angles with the plane on which the observer 
is standing. We will now notice the direction of the lines in a 
square \ym.% fiat upon the same surface upon which the observer is 
standing. 

Place the square at a distance of eighteen or twenty feet from 
the observer, so that a line drawn from the point where the observer 
is stationed, through the center of the square, will divide the front 
line into two equal parts ; the front side of the square will, of 
course, appear longer than the far side, because it is nearer the 
observer. The line receding from the nearest right-hand corner, 
because it forms an angle with the picture plane, appears to tend to 
a point on the left of it, and the line extending from the nearest 
left-hand corner tends to a point on the right of it. These two 
receding lines approach nearer and nearer as they recede from the 
observer, and would, if produced, meet in a point opposite the ej^e of 
the observer (Fig. 16). This point is called the point of sight, and 
it locates the horizon, a horizontal line (page 8) to which all lines 
in a perspective drawing vanish, and on which are situated all van- 
ishing points in parallel and angular perspective. All lines that are 
at right angles to the observer vanish in the point of sight. 

All lines that are at an angle (greater or less than a right 

angle) to the observer, vanish in the 
— horizon, but not in the point of 
sight. 



Fig. 16 represents a square lying flat 
on the surface upon which the observer 
is standing. The point m is opposite the 
observer. 



P.S. Horizon 




a ni b 

ttg, z6. 



CHAPTER III. 



p.s. 



Hor. 



Objects rest upon what is termed the ground plane in many 
different positions, which may be reduced to three general ones. 

I. The objects may be so placed that their surfaces are at 
right angles and parallel with the picture plane. Objects viewed in 
this position are said to be in 
/«ra//^/ perspective (Fig. 17). 

abed represents the picture plane; 
abef represents the ground plane. 
The face hiln and the face parallel to 
it, are parallel to the picture plane; 
the four remaining surfaces are at 
right angles to it. 




Fig. X7. 



2. The objects may be so placed that some of the surfaces are 
at an angle with the spectator, and others parallel with the ground 
plane. Obj ects viewed in this 
position are said to be in «;2- 
^2^/<2r perspective (Fig. 18). 

abed represents the picture 
plane ; abe represents the ground 
plane. When the cube is in this 
position, the faces ijk and ghn 
are parallel to the ground plane, 
and the four remaining sides are at angles with the picture plane. 

3. The objects may be so placed that the surfaces are not par- 

(II) 




Fig. 18. 



12 



Elements and Rules of Perspective. 



P.S 



Horizon 




allel with either the picture plane or the ground plane. Objects 
viewed in this position are said to be in oblique perspective (Fig. 19). 

abed represents the picture plane ; abef represents the ground plane. 

The cube in this illustration is viewed 
in oblique perspective, and the faces 
are at angles with both the picture 
plane and the ground plane. In par- 
allel and angular perspective, the lines 
vanish in the horizon ; but in oblique 
perspective, the lines vanish on lines 
perpendicular to the horizon. 

Oblique perspective is necessary in making drawings of roofs of 
houses, steeples of churches, gables, roads that are not level, etc. ; 
in fact, in all views where there are oblique lines sloping from or 
toward the observer. 

Before proceeding further, it is necessary to define the follow- 
ing terms : 

(Note. — if these definitions are thoroughly understood, and committed 
to memory now, the after-work can be accomplished with very little diflS- 
culty.) 

1 . The ground plane is the plane or surface upon which the 
object or objects to be drawn are situated. 

2. The base or ground line is a horizontal line that marks the 
nearest limit of. the view to be taken ; in a perspective drawing it is 

the lowest line of the picture. 

3. The picture plane is an im- 
aginary plane between the observer 
and the object, and is perpendicular 
to the ground plane (Fig. 17, page 
m&, 20, II, and Fig. 20). 



J ^ . . 


c 


d 








1)\ 


' 



EI.EMENTS AND Rui.ES OF PERSPECTIVE. 1 3 

Fig. 20 represents the ground plane abef, and on the base line ah, the 
picture plane, abed. 

4. The li7ie of direction is a horizontal line extending from the 
e3^e of the observer to the object ; it is perpendicular to the picture 
plane. 

In perspective drawings, the horizon is usually fixed at five feet 
above the base line ; this distance is generall}^ adopted (being about 
the distance from the ground plane to the line of direction) for the 
sake of uniformity. 

In landscapes and sketches, this distance between the horizon 
and base line varies according to the nature of the scene to be rep- 
resented. 

1. In a representation of a low, flat, marshy desert, or of a 
prairie country, the horizon is quite low in order to give the idea of 
a level landscape. 

2. If the picture is intended to convey the idea of great 
height, the horizon is placed low. In a sketch of a mountain gorge, 
cataract, mountain peak, or any scenery where an idea of great 
height is to be given, it is always low. 

3. If an idea of depth, as of a scene viewed from a great 
height, is desired, the horizon is placed high — as the view of a 
city from a tower or steeple, or an expanse of country from a high 
hill. 

4. In an ordinary view where no special height, depth, or dis- 
tance is required, the horizon is placed about one-third the height of 
the picture above the base line. 

5. The horizon is a horizontal line opposite the e^^e of the 
observer, parallel with the ground line, and distant from it five feet. 

6. T'\iQpoi?it of sight is a point on the horizon opposite the eye 
of the observer ; its position on the horizon varies as the spectator 
changes his point of observation. 



14 KlvEMKNTS AND RULES OF PERSPECTIVE. 

7. The prime vertical is a vertical line passing through the 
point of sight. 

8. ^hQ point of station is the point where the observer stands. 
The proper position from which to view the picture, is distant from 
the picture three times the height of the highest object in the 
scene ; or, if the length exceeds the height, then the point of sta- 
tion will be distant from the picture three times the length of the 
object. 

9. Point of distance is a point on the horizon to which all 
measurement lines vanish. In a drawing, it is as far from the 
point of sight as the point of .station is from the point of sight (see 
page 16). 

10. Vanishing points are points in which vanishing lines meet. 

OBSERVATIONS. 

1. Horizontal lines seen obliquely or at angles, if above the 
eye, appear to incline downward; if below the level of the eye, 
they appear to incline upward. 

2. Straight lines may be drawn by finding the position of the 
extremities of the lines. 

3. Curved lines may be drawn by finding their points of inter- 
section. 

4. The center of a perspective square is found by drawing its 
diagonals. 

5. The center of a perspective rectangle is found by drawing 
its diagonals. 

6. The perspective of any surface is determined by the per- 
spective of its boundary lines. 



H 



CHAPTER IV. 



The following frame- work (Fig. 21) is necessary before a cor- 
rect perspective drawing can be made ; the points are placed and the 
lines are drawn in the following order : 

1. Place the point of sight and mark it — P. S. 

2. Through the P. S. draw a horizontal line of indefinite 
length, and mark it — Horizon. 

3. Through the P. S. draw a vertical line, and mark this 
prime vertical — P. V. 

4. Five feet below the P. S. on the prime vertical place a point 
through which draw a horizontal line of indefinite length, and 
divide it off into feet according to the scale. Mark this the base or 
ground line. Measure off on each side of the P. V. 

5. Fix the point of distance on the horizon line, three times 
the height of the object from the 

point of sight, (if the length 
of the object exceeds the height, 
then take three times the length 
to avoid a violent fore-shorten- 
ing) and mark it P. D. 

In this case the supposed 
height of the object is 3^ feet; 
the point of distance is on the 
horizon three times 3^ feet from Fig, zi. 

the point of sight. 

(15) 



p. 



Base or Ground Line. 



Scale Vg, in. to 1 ft. 



Horizon 



i6 



E1.KMKNTS AND RuivKs OF Perspective. 



Another form is here given (Fig. 22) which is often used in 
preference to the one on the preceding page. In this form the 

points are placed and the 
lines drawn as in the form 
on page 15; but the points 
of distance are found by de- 
scribing a half circle, with 
the point of sight as a center, 
and the line extending from 
the P. S. to the point of sta- 
tion as a radius. Where this 
half circle crosses the hori- 
zon, the points of distance 
are located. 



p. D. Horizon 


P. 


s. 


P. D 


\ 1 1 . • I 


Baae_ _ / 


^'^^ 


of, 

a 

Pi 




/ 


Scale 3^ in. to 1 ft. 




> 





Fig. 2Z, 



CHAPTER V. 

RULKS GOVERNING THE DIRECTION OF I.INES AND SURFACES 
OF OBJECTS IN PARAI,I,EIv PERSPECTIVE. 

RUI.E I. All measurements are taken on the base line, which 
is divided into feet according to a given scale. 

RuivE II. All lines parallel to the picture plane are repre- 
sented in their actual position, and do not vanish. 

Rui,E III. All lines perpendicular to the picture plane vanish 
in the point of sight. (P. S.) 

RuiyE IV. All measurement lines vanish in the point of dis- 
tance. (P. D.) 

Rui,E V. All surfaces are governed by the lines that bound 
them, and their perspective is determined by these lines. 

(Note. — After sketching an object or picture, the above rules may be 
applied to test the accuracy of the representation. ) 

In drawing a group of objects in still life or a landscape sketch, 
all the lines should be brought to the test of perspective calculations. 
It is impossible to place the different objects in their proper relation 
to each other, and in perfect harmony with the picture as to size and 
proportions, without a knowledge of the principles of perspective. 
All nature, animate and inanimate, is impressed on the sense of 
vision in accordance with the laws of perspective; consequently all 
art that represents in lines or masses must be in conformity to this 
most important branch of drawing. 

Ele. Pers. — 2. (17) 



i8 



ElvKMKNTS AND RuivKS OF P^RSPKCTIVEJ. 



Perspective admits of another division than that presented in 
this volume — aerial perspective. Aerial perspective has reference 
to atmospheric and other influences, by which objects more or less 
remote are effected in regard to light, shadow, color, gradation of 
tints, etc. , according to their distances and relative positions. The 
principles for guidance in representations in aerial perspective are 
not reduced to systematic rules. A close observance of nature will, 
in time, enable the student to represent these effects with approxi- 
mate accuracy. 



CHAPTER VI. 

REMARKS ON MODKI. AND OBJECT DRAWING. 

Precision is the basis of correct representation from the model. 
All questions are readily and satisfactorily settled by reference to 
the rules and principles oi perspective, vAiv^ are founded on the 
sciences, and are unchanging. (Geometry, Light and Color, and 
Optics. ) 

Practice in model drawing is necessary to satisfactory work in 
sketching from nature. It develops the power of observation, the 
ability to concentrate the attention, and the habit of noticing 
details — their relation to each other and to the whole, and the char- 
acteristic features of the object under consideration. 

The objects used in sketching are geometrical solids, and objects 
based on these forms, supplemented by objects of beauty and util- 
ity. In drawing from the object, all work is free-hand. 

In arranging objects for drawing, they should be placed so that 
the light comes from one side, thus giving the observer a view of 
the shaded side and the shadow. 

The pupil should draw things as he sees them, and not as they 
really are. 

To secure the right proportion in the drawing, the pencil may 
be held at arm's length, and the subtended amount of any dimen- 
sion of the object may be marked on the pencil by moving the 
thumb-nail until the distance between it and the end of the pencil 

exactly covers the desired distance in the object. 

(19) 



20 BiyKMKNTS AND Rui.BS OF PKRSPECTIVK. 

By always viewing the object from the same point of station, 
and holding the pencil (when used as a measure) always at the 
same distance from the eye, and in the same plane, the copy will 
have the same relative proportions as the object. 

SUGGKSTIONS. 

1. Place the model so that the light falls on it from one direc- 
tion only. 

2. Call attention to the facts and the representation of the 
surfaces. 

3. Review rapidly the rules and principles of perspective gov- 
erning the appearance of lines. 

4. Note the distribution of light and shade — high light, 
shade, reflected light, shadow, and reflections, if any occur. 

5. Make the drawing, and if you doubt the correctness of the 
representation, test by perspective. (Rules, page 17.) 

6. The student may draw with board or stretcher at any angle 
that is convenient for him. 

7. In making the drawing for illustration, if the object is not 
at hand, represent the light as falling from the upper left, falling 
on the object at an, angle of 45°; the shade will then be on the 
opposite side. 

8. The shade on objects bounded by plane surfaces is on the 
side away from the light. 

9. When a plane is in shadow, the deepest shade is on that 
part nearest the observer. 

10. Reflected lights appear on the farther side of the plane. 

11. When a plane is in half-light, the highest light on it is on 
the part nearest the observer. 

12. A plane partly illuminated has the deepest shade adjacent 
to the illuminated part. 



Elements and Rules of Perspective. 21 

13. A shadow cast by an object is darker than the shade on 
the object casting the shadow. 

14. The darkest part of a shadow is near the object casting it. 

NoTK. — Test your comprehension of these observations by drawing 
perspectives of a cube, on three different sheets of paper, showing : 
{a) A cubical block. 
{b) A cubical box without the lid. 
{c) A cubical box, minus the front and left or right side. 

15. If the hght falls on a sphere from the left (7), illuminat- 
ing the upper left-hand surface a little in from the apparent edge, 
the deepest shadow is on the lower right side a little in from the 
apparent edge ; near this edge we find a medium tone that is called 
reflected light. 

16. Reflected light on objects having curved surfaces is seen 
on the shaded side. The shaded surface is partially illuminated by 
lights cast from adjacent objects, and from the plane on which the 
object rests. 

17. In cylinders, if the highest light falls on the left side a 
little way in from the apparent vertical boundary, the deepest shade 
comes on the right side a little from the apparent outline. This 
shade is darkest at the top, slightl}^ modified in tone at the base by 
the reflected lights. The top of the cylinder is shaded slightly at 
the left ; the right side is light. The shade and light do not extend 
to the limit of the outline. 

Note. — Drawings may be finished by hatching, stippling, or shading 
with the stump. 



CHAPTER VII 

RKFLKCTIONS. 

Rkflkctions are produced ( i ) by polished surfaces that give 
back form and color, as mirrors, etc.; (2) by polished siurfaces that 
give reflections somewhat distorted, as chinaware; (3) by liquids at 
rest — the smooth surface of the liquid serving as a mirror. 

The rule that covers all reflections is, — 

The angle of incidence equals the angle of reflection. 

To place reflections in perspective, treat the reflections as 
realities. Such objects as rise or occupy a position perpendicular to 
the surface of the water, preserve their real proportions and relative 
positions. Thus posts, perpendicular cliffs, and masts of boats, 
throw their reflections to their full height, while surfaces that recede 
from us — foreshortened surfaces — although much higher in reality, 
and rising far above the objects mentioned, may scarce be seen at 
all in the reflection. If the point of sight is placed on a level with 
the water line, then the reflection will be a perfect repetition of the 
view, but the slightest elevation of the point of sight above the 
water line affects everything reflected that is not perpendicular to 
the water's edge. For instance, a roof jutting out over a boat- 
house on the bank will be much longer in the reflection than the 
vanishing lines in the original, and from the point of view we may 
see the top of the roof, while in the reflection we may see the under 
side of the projecting part of the roof. The reflection of an arch 

f22) 



Elements and RuIvKS of Perspective. 23 

or culvert will be exactly like the original in the general face of the 
arch, but on account of the position of the observer he sees only 
the under side of the arch in the reflection. 

The same rules that apply to linear perspective, apply to the 
perspective of reflectionc. 



CHAPTER VIII 

Problkm. — Place in perspective a 3-foot cubical box, the front 
line of the cube resting on the base line, and the nearest corner of 
the cube 3 feet to the left of the prime vertical. 



I 



Point of Distance ( 9 Ft.) 



Horizon 




Scale M in. to 1 ft 



t^g. ^3' 



1. Locate the point of sight. If the object is on the left of 
the prime vertical, fix the point of sight on the right side of the 
paper. If the object is on the right of the prime vertical, then 
locate the point of sight near the left edge of the paper. 

2. Draw the horizon, prime vertical, and base lines, marking 
the base line off according to the given scale. 

3. lyocate the point of distance. (Page 15.) 

As the cube is 3 feet on the left of the prime vertical, move 3 
feet to the left on the base line, and mark the point a; from a move 

3 feet further to the left, and mark the point d (Rule I). From a 

(24) 



EI.KMENTS AND RULES OF PERSPECTIVE. 



25 



and b, rule lines to the point of sight (Rule III). We now have 
the side ab and two sides of the base extending back from the front 
line ; to determine the length of these receding lines is the next 
step. 

As lines of the same length at different distances appear of dif- 
ferent lengths, we know it is impossible to measure three feet on 
these lines, so we take the measurement on the base line (Rule I), 
and from the measurement point to the point of distance rule a 
line. Where this line crosses the line receding from a, the point c is 
located ; from the point <:, draw a line parallel to ab, mark the point 
d, and we have the base of the cube. 

J^rom a and b, draw vertical lines 3 feet in length, and draw ef 
(Rule II). 

From e andy, draw lines to the point of sight (Rule III), erect 
vertical lines from c and d, and where these touch the lines receding 
from e and/" locate the points g and h, and draw the line gh which 
completes the outline of the cube. 

ProbIvEm. — Place in perspective a box 6 feet high, with a base 
3 feet square, the nearest corner of the base 7 feet to the right of 
the prime vertical on 
the base line. 

From the point 
where the base line is 
crossed by the prime 
vertical, move to the 
right on the base 7 

feet, because the nearest corner of the box is 7 feet to the right of 
the observer, and locate the point a. From this draw the line ab on 
the base 3 feet long. From a and b, draw lines to the point of sight 
(Rule III). From the point a, move toward the point of sight 3 
feet, and draw a line from the point of measurement to the point of 



p. 


''^ •_-======^ 




' ^\ 




f . Horizon P.„D. 




, . .^ 


^ 


xr 


c 






\ 






Base 

11 ,,11.. 




111 




i 


1 


J 



Tig. 24' 



26 



Klemknts and RuIvBS of Pkrspectivk. 



distance. Where this line crosses the line receding from a, we have 
a point 3 feet from a. Mark this point d, and from it draw a line 
dc parallel to the front line of the base. This gives the square abed 
in perspective, the base of the box. From a and b draw vertical 
lines, each 6 feet high, and draw the horizontal line ef; from e and 
/ draw lines to the point of sight (Rule III). As the points e 
and f are above the level of the eye, the lines receding from them 
appear to incline to the horizon. 

From the point d, draw a vertical line to the line receding from 
e, and mark this point h; and from c, draw a line to the line reced- 
ing from y", and mark it g. Connect h and g, and we have the 
square forming the top of the box, 

ProbIvKm. — Place in perspective a box 5 feet long, 3 feet high, 
and 3 feet wide, 4 feet to the right of the observer, and 2 feet 
back from the base line. 



p. 8. 



Horizon 



P. D. 




i^'g. 25. 



lyocate the points and draw the lines as in the preceding 
problem. As the object is 4 feet to the right of the prime vertical 
line, count on the base line 4 feet to the right (Rule I), and place a 
point and mark it a . As the object is 5 feet long, move 5 feet 
further to the right, and fix the point b' ; and from these two points 
draw the lines receding to the point of sight. The box is not on 



Elements and Rules of Perspective. 27 

the base line, but 2 feet back from it; in order to find the points for 
the front line of the box, we measure 2 feet on the receding line a, 
according to Rule IV, and locate the point a. We then draw the line 
ab; according to the same rule, fix the point d, and draw the line 
dc. According to Rule II, draw the lines representing the front face 
of the box. Because the sides of the cover are perpendicular to the 
picture plane, the lines from e and / vanish in the point of sight ; 
from the point d, draw a vertical line to the line vanishing from e ; 
from this point h, draw a line parallel to ef, and draw the line eg. 



CHAPTER IX. 



Probi^km. — Place in perspective a circle 4 feet in diameter, 7 
feet to the left of a prime vertical, the circle tangent to the base 
line at that point. 




cbfe = geometrical 
cbgh = perspective 



If a circle is placed opposite the eye, the diameter on a level 

with the horizon, it will be represented by a straight line ; if it is 

directly opposite the observer at right angles with the ground plane, 

the circle is represented by a vertical line; if the center is directly 

opposite the eye, it will be represented by a perfectly round figure ; 

but in any other position the circle will be represented by an ellipse 

(Fig. 26). 
(28) 



EivKments and Rules of Perspectivk. 



29 



Now place the 4- foot square cdef in perspective (page 28), and we 
have the figure cbgh; then draw the diagonals eg and bh. From the 
point h, move toward the prime vertical 2 feet, and draw a line to 
the point of distance ; this line divides the line bg into two parts. 
From i draw a line parallel to cb^ and from «, 4, and 3, draw lines to 
the point of sight. When these lines are drawn, we have the eight 
points through which the circle passes located, and all that remains 
to be done is to pass a curved line through these eight points, and 
we have a circle, 4 feet in diameter, in perspective. 

In order to place circles, triangles, hexagons, etc., in per- 
spective, it is first necessary to draw a geometrical plan below the 
base line in order to locate certain points through which to draw the 
outline of these figures. 



Hor 



P..D. 



P.S. 




ml 2 



Before proceeding to place the circle in perspective, draw a 4-foot 
square below the base line (because the diameter of the circle is 4 
feet), and in this draw a circle tangent to the four sides of the 



30 Elements and Rui^ks of Perspective. 

square; draw diagonals across the square, and through the points 
where the diagonals and circle intersect, draw the lines 3 and 4 to 
the base line ; draw ad. 

PROBI.EM. — Place in perspective a hexagon with a diameter of 4 
feet, touching the base line at a point 9 feet to the left of the P. V. 

In this problem the square abmp is placed in perspective. Then 
the circle is drawn, and placed in perspective. In order to draw 
the hexagon, divide the vertical diameter into four equal parts, and 
from the first and third division points in this line draw horizontal 
lines to the points h and d, and g and e; from the point c, draw ck 
and cd ; from f draw fe and fg. Connect the points g and h 
and d and e, strengthen these outlines, and the hexagon in the 
ground plane is completed. 

Prolong the lines gh and ed until they reach the base line at 
the points i and 4, and from these points draw lines to the point of 
sight; in these lines the perspective of the sides ed and gk of the 
hexagon will be found. In the perspective circle locate the points 
corresponding to the points cdefgh in the ground plan, draw the 
lines connecting these points, stengthen them, and the hexagon is 
drawn in perspective. 

Probi^em. — Place in perspective 5 feet from the observer a 
circle whose vertical diameter is 3 feet, and 2^ feet from the base 
line, and whose horizontal diameter is at R. A. to the picture plane. 

It is necessary to understand this problem before a box with an open 
cover can be drawn correctly. 

If the horizontal diameter is at R. A. to the picture plane the 
perspective circle is in a square that is at R. A. to the picture plane. 
To locate this square it is necessary to first draw the ground plan. 

As the circle is at a distance of 5 feet from the observer, move 
off on the base line 5 feet from the prime vertical, and from this 



Elements and Rules of Perspective. 



31 



P.S. 



Horizon 



P.D. 




Mg. 28. 



point e, draw a line to the point of sight; in this Hne from e 
will be found a line parallel to the horizontal diameter, and one 
side of the perspective square. 

To find the per- 
spective of the side of 
the square that is par- 
allel to the horizontal 
diameter, erect from the 
point e a vertical 
line 3 feet high, and 
from this to the point 
of sight, draw a line; 
in this line we find the 
upper side of the per- 
spective square. The 
horizontal diameter van- 
ishes in the point of sight, and in the drawing is represented by 
a line from x (a point i}4 feet above e) to the point of sight. 

The problem states that the vertical diameter is 2 ^ feet from 
the base line, on the line receding from e. In order to locate this 
point, move from e toward the prime vertical 2}4 feet (Rule I), and 
fix the measurement point 3'; from this to the point of distance 
rule a line, and at the point where this line crosses the line reced- 
ing from e, locate a point (3), and from this point erect a vertical 
line until it meets the line receding from m. This is the vertical 
diameter of the circle. Before proceeding, the ground plan must be 
drawn — the square, diagonals, circle, and the lines from the points 
where the diagonals and circle intersect. As the diameter is 3 feet, 
move from the point 3, i^ feet each way, and locate a' and b on 
the base line; finish the ground plan, and from a' and b\\ and 2, 
draw lines to the point of distance. Where these lines cross the line 



32 



KlvEMENTS AND RULBS OF PERSPECTIVE. 



receding from e, points are located that correspond to points in the 
plan; from these points erect vertical lines until they meet the line 
receding from m^ and draw diagonals. We now have the square 
abed at R. A. to the picture plane; in this square, draw the circle 
through the points located by the ground plan, and strengthen the 
outlines. 




Line on which the meas . 
of the sq. above the eye 
are taken. 



1 



1^^. 29' 



Problem. — Place in perspective a circle 3 feet in diameter, 
7 feet on the right, and 5 feet above the eye of the observer. 

Draw the square adcd 7 feet on the right of the observer on the 
line X. From a and 3 draw lines to the point of sight (Rule IV). 
From a move off toward the prime vertical 3 feet, and draw a line 
to the point of distance. Locate the point d, and draw a line from 
d parallel to ad. 

lyocate the points in the perspective square, and draw the circle 
by points, located by the lines in the actual view. 



CHAPTER X. 



Problem. — Place in perspective a pyramid 6 feet high, with 
a base 4 feet square; the front Hne of the base on the base Hne, 
the nearest comer 6 feet to the right of the observer. 



p.s 




JEig. 30. 

Place the base of the pyramid, the square abed, in perspective, 
according to page 25. 

The apex of the pyramid is directly over the center of the 
base, and its perspective height is found by erecting a vertical 6 
feet from the point b to the point e. 

Draw the square efgh above the horizon, draw diagonals, and 
at the point on the square where they cross, locate a point which 
marks the top of the pyramid. 

Draw diagonals across the base abed. The point where they 
cross marks the center of the base. A line drawm from this point to 
the center of the upper square marks the vertical height of the 
pyramid, and lines draw^n from the corners abed to the apex, form 
the sides of the pyramid. 



Ele. Pers. 



(33) 



34 Elkmknts and Rules of Pbrspectivk. 

ProbIvEm. — (Figure 31.) A small two-story house in parallel 
perspective, situated about 45 feet on the right of the observer; and 
extending back from the picture plane about 28 feet. The front 
has three windows and a door. The windows in the upper story 
are 5 feet high and 2}^ feet wide. The windows on the lower floor 
are 6 feet high and 2^ feet wide. The door is 7 feet high, and 3 
feet wide. The vertical height of the roof is 5 feet. 

Prepare the form according to page 15. Draw the lines repre- 
senting the front of the house abed. From a and c, draw lines to the 
point of sight; from a point 28 feet to the left of the point <2, to a 
point on the horizon 60 feet from the point of sight, rule a line. 
Where this crosses the vanishing line a, fix the point ^, and draw 
ef. From the center of cd erect a perpendicular 5 feet long ; place 
the point g\ and draw eg and dg in order to get the direction 
of the end of the roof parallel with eg. It is necessary to draw a 
vertical line uv across the horizon about 10 feet to the right of the 
point 2. Prolong the lines eg and gd until they meet this line; the 
line eg meets this vertical at a point not represented on this page. 
To this point, rule a line from /, and from g draw a line to the 
point of sight; this line is parallel to fe and ae, and vanishes in the 
same point. At the point where the line receding from g crosses 
the line from/", mark the point h — the point of the gable at the back 
of the house. All measurements for the windows and door must be 
taken on the base line, and on the line ae. The tops of the second 
story windows are 2 feet from the roof; so mark a point m 2 feet 
from e, and from this draw a line to / and another to the point of 
sight. As the upper windows are 5 feet high move down 5 feet to 
the point n;and draw ^*, and nr to the point of sight. From n, 
move down i foot; draw ok, and os to the point of sight. As 
the lower windows are 6 feet high move down 6 feet, and from 
p draw p^ and os to the point of sight. Now draw the lines rep- 



ElvKMBNTS AND RULKS OF PKRSPECTIVK. 



35 



resenting the sides of the windows. 
Those in the front of the house are 
2^ feet apart, and the spaces between 
the sides of the front and the windows 
are i ^ feet on each side. According 
to Rule II, draw the Hues 3, 4, 5, and 
6. The first window on the side is 4 
feet from the corner of the house; to 
fix the Hne 7, 8, move from a 4 feet to 
the left, and rule a line to the point of 
distance. Where this line crosses the 
line receding from a, locate a point, 
and from this point erect a vertical 
line; this marks the right line of the 
windows. As the windows are 2 ^ feet 
"wide, move 2^ feet further toward the 
point of sight, and locate a point; from 
this, rule a line to the point of distance. 
Where this crosses the line receding 
from a, erect 'a vertical; in this verti- 
cal 9, 10, we find the other side of the 
window. In this same manner draw 
the vertical sides of the remaining 
windows. As the door is 3 feet wide, 
measure three feet on the base, and 
draw the vertical lines representing 
the sides of the door. After all these 
general lines are drawn in, draw in 
the lines representing the panels of 
the door, and the sashes of the win- 
dows. 



Prime Vertical Line. 




^*^. 5 J. 



CHAPTER XI. 

ProbIvKm. — Place in perspective a room 14 feet wide, 15 feet 
deep, and 9 feet high, front line of floor being on a line with the 
base. (The observer is stationed at a point half way between the 
points a and b^ and 5 feet from the base line. ) 

As the observer is at a point 5 feet from the base line, locate the 
point of distance on the horizon at a distance of 10 feet from the 
point of sight, having first drawn the prime vertical and base lines. 

As the room is 14 feet wide, move 7 feet each way from the 
point where the prime vertical crosses the base, and locate the 
points a and b. From these points draw af and be 9 feet high to 
represent the side walls of the room; then draw ef, which rep- 
resents the front line of the ceiling. 

Then draw the lines from abe and f to the point of sight. To 
find the depth of the room, which is 15 feet, move from the point b 
15 feet to the left, and locate the point m. From this, rule a line to 
the point of distance; where this crosses the line receding from b, 
locate the point r, and draw cd parallel to the base line. This line 
represents the line made by the floor and back wall of the room. 
From c and d, draw vertical lines to the lines receding from e and/, 
and where these lines meet, locate the points g and h. We now 
have abed, representing the floor of the room, 15 ft. x 14 ft. 

bche representing the right wall of the room, 9 ft. x 15 ft. 

adgf representing the left wall of the room, 9 ft. x 15 ft. 

cdgh representing the back wall of the room, 9 ft. x 14 ft. 

efgh representing the ceiling of the room, 14 ft. x 15 ft. 

(36) 



EI.KMKNTS AND Rui.ES OF PERSPKCTIVK. 



37 




^g. 52. 



38 ElvKMKNTS AND RULKS OF PBRSPKCTIVE. 

On the right side of the room are two windows, 3 ft. x 5 ft. , 
3 feet from the front line of the wall, and 3 feet apart. In the left 
side a door, 8 ft. x 3 ft. , 5 feet from the nearest line of the left wall. 

To find the perspective of the door and windows, it is neces- 
sary to take the measurement on the base line, and on the lines af 
and be. The width of the windows is found by drawing lines from 
each foot on the base line to the point of distance; where these lines 
cross be they mark the line off into perspective feet. As the first 
window is 3 feet from the nearest line of the right wall, move 3 feet 
from b, and follow the line until it meets the line be ; mark this 
point 3, and erect a vertical line (Rule I). In the same manner, 
locate the point 6, leaving a space of 3 feet from the point 3 — the 
width of the window — and erect a vertical line (Rule I). 

Follow the lines 9 and 12 until they meet cb. Mark the points 
where they cross 9 and 1 2 , and from these draw the vertical lines 
representing the sides of the second window. 

As the windows are 5 feet high and 2 feet from the floor, move 
up the line be 2 feet, and locate the point k; then move 5 feet 
further, and locate the point /. From these points k and /, draw 
lines to the point of sight; where these lines cross the lines reced- 
ing from 3, 6, 9, and 12, the points for the upper and lower lines of 
the windows are located. Strengthen the outlines of the windows 
in perspective, and proceed to draw the outlines of the door on the 
left side of the room 

The door is 8 ft. x 3 ft., and 5 feet from the nearest wall of 
the room. The points x and v are found as the points 3, 6, 9, and 
12 are found; the height is found by ruling a line from p to the 
point of sight; where this crosses the vertical lines from x and v, 
we find the top of the door. Strengthen the outlines xvyz, which 
form the perspective outlines of the door. 



ElvEMENTS AND RULKS OF PERSPECTIVE. 



39 




^g- 33- 



Problem — (Figure 33). — A view of the left side of a room. 
The half -open door is 4 ft. x 8 ft. (frame 6 in. ); the nearest corner 
4 feet from the line cd (the drawing is made according to pages 17 
and 28). 



40 



KI.KMKNTS AND RUI.KS OF PERSPKCTIVK. 



PROBI.KM (Figure 34). — View of a tiled floor 8 ft. x 14 ft. 
The position of the observer is supposed to be half way between the 
two walls of the hall. 



f 




(Measurement point lo feet to left of Prime V.) 
Pig. 34 



In this figure, the point c is located by a line extending from 
m (a. measurement point on the base line 14 feet from ^) to the 
point of distance. 



CHAPTER XII. 



ProbIvKM. — Find the per- 
spective height of a 3-foot verti- 
cal Hne, 5 feet back from the 
base line, and 4 feet from the 
observer. 

Problem. — Find the per- 
spective of a point 7 feet from 
the observer, and 3 feet from the 
base line — the point of station, 
7 feet. 

Note. — The required point is at a. 

Problem. — Place in per- 
spective a horizontal line 4 feet 
long, at right angles with the 
picture plane, the nearest end 4 
feet from the base line and 5 
feet from the prime vertical — 
station point 7 feet. 

Problem. — Find the center of 
a 4 -foot square standing on the 
right of the observer at right angles 
to the picture plane at a point 3 feet 
from the prime vertical — point of 
station 8 feet. 




Pig. 35. 



Hor. 




Fig. 36. 











- 








PD. 






|\ 


S^ 


^ 




^ 


/ 


X 


\ .... 




m 


va 




a 
Fig. 37- 





I 


>.S. 








Hor. 




V 


^ 


b 


d 


^ 




\ 


\ 


\ 


y^ 






^ 


.b^ 


\ 






^ 


y 


^ 




Base 


m 








\ 





Fig. 38. 

{abed required square, o center.) 
(41) 



42 



EI.BMENTS AND RuivKS OF PERSPECTIVE. 




f 



Line by which the perspective 
height of the cross is obtained. 



Fig' 39- 



Probi^em. — A skeleton cross 8 feet high, with a base 2 feet 
square. The cross piece is 2 feet below the top of the cross, and is 
formed by two 2- foot cubes, one on each side of the standard. The 
base is 6 feet square, and i foot high; the front line of the base 
rests on the base line, 6 feet to the right of the observer. 



ElvKMKNTS AND Ruizes OF PERSPECTIVE. 43 



EXPLANATION OF FIGURE 39. 

As the nearest corner of the base is 6 feet from the observer, 
move out on the base Hne to the right of the prime vertical 6 feet, 
and locate the point a. From this draw the line ab coinciding with 
the base line, and draw the base according to Rules I, II, III, 
and IV. 

As the base of the standard is a 2 -foot square, and is situated 
over the center of the base, it is necessar}^ to divide the upper 
surface of the base into 2 -foot squares; this is done by drawing lines 
to the point of sight, and to the point of distance, according to 
Rules III and IV. 

As the standard is 8 feet high, and 2 feet back from the picture 
plane, its perspective height is measured by a line drawn from p to 
m. From m a line is drawn to the point of sight, and in this line we 
find the top of the standard (z) by drawing a vertical line from the 
point r until it meets the line receding from ni. 

Draw ik and rv parallel to ab (Rule II). From v, draw the verti- 
cal line vk, and from k draw a line to the point of sight (Rule III). 
From t draw //. From / draw a line to the point of sight (Rule 
III)^ and draw sj. 

As the cross piece is 2 feet from the top of the standard, move 
down from the point 7n 2 feet, and rule a line to the point of sight; 
w^here this crosses the line ri locate the point x, and through this 
draw a horizontal line of indefinite length. 

The perspective length and wadth of the cross piece is deter- 
mined by the base. The square of the base is divided into nine 
2 -foot squares, and the left cube of the cross piece is over the middle 
square in the left-hand row, and the right cube of the cross piece 
is over the middle square in the right-hand row. 



44 Elements and Rules of Perspective. 

To determine the length of the line from x, draw lines from 1 1 
and 12 (middle square in left-hand row), and from 13 and 14 (mid- 
dle square in right-hand row), to the line from x, and locate the 
points 2,3, 4, and 5. 

From 2 and 3, draw lines to the point of sight, and where these 
cross the lines from 12 and 13, locate the points 6 and 8. 

As the cross pieces are 2-foot cubes, the length of 3, 5 is 
obtained by moving 4 feet from the point m, and drawing a line to 
the point of sight. As this line just drawn coincides with the hori- 
zon, the points 4, 5, 7, and 9 are on the horizon, and are determined 
by the lines from 11, 12, 13, and 14. 



CHAPTER XIII. 

Problem. — Place in perspective a box 5 feet long, 3 feet wide, 
and 3 feet high, 7 feet to the right of the prime vertical. The 
cover of the box one-quarter open. (See page 31.) 




Fig. 40. 



EXPLANATION OF FIGURE 40. 



Draw the box according to rules governing the lines of objects 
in parallel perspective. 

(A box-lid in opening all the way describes a half circle; in 
opening half way, one-fourth circle, and in opening one- quarter 



(45) 



46 KI.EMKNTS AND RUI.KS OF PKRSPKCTIVK. 

way, it describes one - eighth of a circle. Three - fourths open is 
defined by three -eighths of a circle). 

In order to represent a lid open one-fourth of the way, it is 
necessary to construct a half circle in perspective. This is done by 
constructing a half circle below the base line extending from the 
point a to the left, a distance of 6 feet. (The box-lid is three feet 
wide, and represents the radius of the half circle. ) 

Draw the half circle, and from it locate the point for the per- 
spective half circle; from f \.o x, and from ^ to _y, represents one- 
eighth of a circle. If the points -^ and j/ are connected, and lines 
drawn from these points to g and h, we have the cover of the box 
one-quarter open. 



CHAPTER XIV. 



ANGUI.AR PKRSPKCTIVK. 




F^g. 41- 



In taking an angular view, we do not have a 
full view of any of the surfaces. The faces that are 
at angles to the picture plane recede from the spec- 
tator; sometimes at equal angles, and sometimes 
at unequal angles. The lines bounding the surface 
that is least foreshortened, vanish in a point fur- 
ther from the object than those of the surface that has a more decided 
foreshortening. When the two surfaces form equal angles with the 
picture plane, the vanishing points for the lines that bound these 
faces are equally distant from the point of sight; but as the object 
is turned, and its position with regard to the picture plane changed, 
the position of the vanishing points, with regard to the point of 
sight, changes. The surface that forms the greater angle with the 
picture plane has a more violent perspective, and the lines come to 
a point on the horizon nearer the point of sight, than those lines 
of the surface that makes a smaller angle with the picture plane. 
All objects in parallel perspective are at R. A. to the picture plane, 
or they stand at an angle of 90°. In angular perspective they are 
placed at any angle from 90° to 1°. 

All those surfaces that are at an angle of 45° to the picture 
plane vanish in the point of distance. If the line vanishes from 
right to left, it vanishes in the point of distance on the left. If it 

recedes from left to right, it vanishes in the point of distance on the 

(47) 



48 



ElvEMKNTS AND RuivKS OF PBRSPKCTIVE. 



right. If an angle of 7nore than 45° is formed by the surface and 
picture plane, the vanishing point is between the point of distance 
and point of sight. If an angle of less than 45° is formed by the 
object and picture plane, then the vanishing point is beyond the 
point of distance. 




Point 



l^ig. 42. 



The squares abed (Fig. 42) are in parallel perspective ; the lines ad and 
be recede from the picture plane at angles of 90°, and vanish in point of sight. 
(Each square has four right angles, and each R. A. measures 90°. By actual 
test, the student can satisfy himself that the diagonal of a square divides the 
angles into equal parts, each part measuring 45°.) If diagonals are drawn 
across these squares, they meet in the points of distance. In Figure 42, the 
angle bad measures 90°, and the receding side ad forms an angle of 90° with 
the picture plane, and vanishes in the point of sight. The diagonal ae divides 
the angle bad into two equal parts (this forms two angles of 45°), and vanishes 
in the point of distance. 



Elements and Ruizes of Perspective. 



49 



Before a perspective drawing in angular perspective is at- 
tempted, it is well to have the following form understood. 



P.D. 50"* 




i^*^. 43- 



The points adcd, etc. , on the horizon are the points to which 
lines that recede from the picture plane, at 8o°, 70°, 60°, 50°, etc., 
vanish. If an object makes an angle of 80° with the picture 
plane, the vanishing point for this, and all receding lines parallel to 
this, will be found on the horizon at the point a; if the face forms 
an angle with the picture plane of 70°, 60°, 50°, the vanishing 
point for these lines will be on the horizon at the points 70°, 60°, 
50°; at an angle of 45° in the point of distance, any angle formed 
by the receding lines less than 45° is beyond the point of distance 
on the horizon. These points in the horizon are found by con- 

Ele. Pers. — 4. 



50 BI.KMKNTS AND Rui.KS OF PERSPECTIVK. 

structing angles at the point of station. These angles are found 
in the following manner: 

Through the point of station rule a line (parallel to the base 
line) forming two right angles or i8o°. This space is divided 
into angles by the protractor, which is placed on the horizontal Hue, 
extending through the station point, with the point on the pro- 
tractor marked 90° on the prime vertical; the points representing 
the angles 80°, 70°, 60°, etc., are marked on the paper by means of 
dots; then through these dots, from the point of station, lines are 
ruled to the horizon, where they locate the points, forming angles 
on the horizon equal to those at the point of station. 

NoTB. — The angles at the station point are called the actual angles ; the 
angles at the horizon are called perspective angles. 



CHAPTER XV. 

RUI.ES GOVERNING THE DIRECTION OF I,INES AND SURFACES 
OF OBJECTS IN ANGUI.AR PERSPECTIVE. 

Rule I. All lines bounding surfaces that are at an angle of 
^5° to the picture, vanish in the point of distance. 

Rule II. All lines bounding surfaces that make an angle with 
the picture plane greater than 4^° , vanish between the point of dis- 
tance and the point of sight; the greater the angle at the picture 
plane, the nearer the vanishing point to the point of sight. 

Rule III. All lines bounding surfaces that make an angle of 
less than ^5° with the picture plane, vanish in a point on the hori- 
zon beyond the point of dista7ice. The less the angle at the picture 
plane, the further the vanishing point is from the point of distance. 

Rule IV. All measurement points are located on the base 
line by means of the ground plan. 

Rule V. All measurement lines vanish in the vanishing points. 

Rule VI. The vanishing points in the horizon are found by 
means of angles at the station point. These angles are drawn, and 
points ascertained in the following manner: 

Through the station point, rule a line parallel to the base line; 
place the protractor on this line, with the point of the protractor 
marked 90°, on the prime vertical; then mark the required angle 

(51) 



52 Klemknts and Rui.es of Perspective. 

on the paper, and from the station point draw a line through this 
dot to the horizon. This point on the horizon is a vanishing point 
for all lines that recede from the picture plane at the same angle as 
that which was drawn at the station point. 

If an angle of 20° is measured, and a line drawn to the hori- 
zon, the point on the horizon marked by this line is the vanishing 
point for all lines receding at an angle of 20°. 



I 



CHAPTER XVI. 



ProblKm. — Place in perspective a 3-foot square, 5 feet to the 
right of the observer, the corner resting on the base line, and the 
nearest side receding from the picture plane at an angle of 45°. 



P.D. 



P.D. 




Pig' 44- 

As the nearest corner touches the base line 5 feet to the right 
of the observer, move 5 feet to the right of the prime vertical and 
locate the point a. After locating this point, proceed to draw the 
ground plan in the following manner: 

Through the point a, draw a vertical line of indefinite length, 

(53) 



54 



BiyKMKNTs AND Rules of Perspkctivk. 



and at the base line construct a right angle with the protractor by 
placing the point marked 90° on the vertical, and the horizontal 
edge on the base line. 

After the angle is constructed, draw the square in the ground 
plan; from a, draw lines to the points of distance.' (Rule I.) To 
locate a point 3 feet from a on the right, and one the same distance 
toward the left on the receding lines, place the measurement points 



p,s 



p.i>. 




Fig. 45. 

e and/ located by means of the ground plan. (Rule IV.) From 
these draw lines to the points of distance; where these cross the 
lines from a, mark the points d and b, and where the lines from 
e and / to the points of distance intersect, mark the point c, and 
strengthen the outlines of the square abed, at an angle of 45°. 

Probi^km. — Place in perspective a rectangle, 5 feet by 3 feet; 
the nearest corner 5 feet to the left of the prime vertical, at an angle 
of .45°; the longest diameter of the box extending from a toward 
the point of distance on the left. 



Elements and Rules of Perspective. 



55 



Locate the point a, draw the hnes to the points of distance, and 
draw the rectangle abed, geometrically , with the longest diameter 
extending from a toward the left. 

Prolong cd to the base line, and prolong cb to the point e. These 



Horizon 




Station Pcint 



Tig. 46. 



points locate the measurement points for the lines receding from 
a. From e and /, rule lines to the points of distance, and where 
these cross the lines receding from a, fix the points b and d. 
Strengthen the outlines of the rectangle abed in perspective at an 
angle of 45°. 



56 ElyEMENTS AND RuLES OF PERSPECTIVE. ' 

ProbIvEm. — Place in perspective a 4-foot square, 6 feet to the 
right of the observer, and 3 feet back from the base line, at an 
angle of 45°. 

lyocate the point a. In this case the square is 3 feet from the 
base line, so it is necessary to move from the point a^ 2> f^^t down in 
a vertical direction, and fix the point a. Through this rule a line 
parallel to the base line; place the protractor on this line, and draw 
the right angle at a and complete the 4-foot square. Find the per- 
spective of the point a in the following manner: locate the meas- 
urement points I and 2; prolong the lines da and ba until they 
meet the base line; from i and 2 rule lines to the points of distance; 
where these measurement lines cross, we have the perspective of the 
point a ; from a rule the vanishing lines to the points of distance; 
prolong cd and cb until they meet the base line at e and f (measure- 
ment points). From the points e and/", draw measurement lines to 
the points of distance; where these lines cross the lines receding 
from a^ mark the points b and d ; from these points, rule lines 
to the points of distance; where they cross, mark the point c. 
Strengthen the outlines of the square abed. 



CHAPTER XVII. 



ProblKM. — Place in perspective, at an angle of 45° to the 
picture plane, a rectangular box, 10 feet long, 4 feet wide, and 3 
feet high, 7 feet to the right of the observer. The longest diameter 
of the box is from the point a toward the point of distance on the 
right. 



p.s. 



Horizon 



P«.l>. 




1^'^. 47' 



(57) 



58 EiyEMKNTs AND Rules of Perspective. 

lyocate the point a, draw the plan abed geometrically, and from 
a to the points of distance, draw lines. (Rule I.) Prolong cd 
and cb to the base line, and where they touch, locate the points of 
measurement e and f. From these points draw lines to the points 
of distance, crossing the lines receding from a at the points b and d, 
and mark the point e^ which completes the base. From a erect a 
vertical line 4 feet, and mark the upper point g ; from g rule lines 
to the points of distance. (Rule I.) Erect vertical lines from b and 
d, and where these vertical lines touch the lines vanishing from g^ 
mark h and k. From these points rule lines to the points of 
distance. Strengthen the outline of the perspective drawing of the 
box at an angle of 45°. 



EiyEMENTs AND Rules of Perspective. 



59 




ProbIvEm. — In this illustration (Fig. 48), the view is supposed to be taken 
from a point 3 feet to the left of the point where the cross touches the base 
line. The side near the observer recedes at an angle of 30° ; dimensions same 
as in Fig. 39. 



6o 



KlvKMKNTS AND RuivKS OF PKRSPECTIVK. 



Problem. — View of a tiled floor, 8 ft. x 14 feet. Viewed at an 

angle of 35°. 

lyocate the point a, and construct the ground plan abed at an 
angle of 35° to the base line. 



P.P. for Unea ai an -angle of a6° T 3. 




r^g. 49' 



At the point of station, construct the angles of 55° and 35°; 
from these angles draw lines to the horizon, and locate the vanish- 
ing points for the receding lines. 

Draw the lines from d and d of the plan until they meet the 
base, and mark these measurement points ^ and /. From these 
points, rule lines to the points of distance, and where they cross 
locate the point c. 

The tiles in the floor are i foot square; to divide the perspec- 
tive floor into these tiles, lines are ruled from each foot in the line 
ad of the plan, to the base line — to the points i, 2, 3, etc. From 
these points, lines are ruled to the vanishing point on the left. 



Kl^KMENTS AND Rui.KS OF PERSPKCTIVEJ. 



6l 



From each foot on the line ab, lines are ruled to the base, and from 
these measurement points lines are ruled to the vanishing point on 
the right. The lines vanishing to the left, and those vanishing to 
the right cross and divide the floor off into i-foot tiles, which may- 
be tinted according to the taste. 



MO^^^?" 



n^-«t 



ro\^^ l^^\^ 




mg. 50. 

Note. — 2 «, line by which the perspective height is determined. Explain Fig. 50. 



CHAPTER XVIII. 

SKCOND METHOD FOR PIvACING AN OBJECT IN ANGULAR PER- 
SPECTIVE WITHOUT A GROUND PLAN, BY MEANS OF 
MEASUREMENT POINTS ON THE HORIZON. 

Rule I. Construct the angles at the station point, and by 
these locate the vanishing points on the horizon. Determine the 
measurement points on the horizon by means of the points of ' dis- 
tance, and from the base line to these points, draw lines to deter- 
mine the width of the object. 

Rule II. To find the measurement point on the r^^^ of the 
point of sight, move out on the horizon, as far from the point of 
distance on the left as the distance from the point of distance to the 
station pointy. :: 

Rule III. To find the measurement point on the left of the 
point of sight, move out on the horizon from the point of distance 
on the right as far as it is from the point of distance to the station 
point. 

Problem. — Place in perspective a 3-foot cube, touching the 
ground line at 5 feet to the right of the observer, the sides receding 
at an angle of 45°. 

Draw the form as given on page 16; then, according to Rule I, 

draw the line be through the station point a, and mark off at the 
(62) 



EI.KMKNTS AND RuIvE:S OF PKRSPECTIVK. 



63 



point of station, an angle equal to the angle at which the side of the 
object recedes from the picture plane; and where this line cuts the 
horizon is the vanishing point for the faces of the cube that are at 



Horizon 




Pig- 51- 

an angle of 45° to the picture plane. As the corner touches 5 feet 
to the right of the observer, move 5 feet to the right of the prime 
vertical, and mark the point d ; as the two sides recede at an angle 
of 45° to the picture plane, draw lines from d to the points of dis- 
tance. 

The next step is to determine the length of these lines. As they 
are receding lines, we measure them on the base line (Rule I). 
Before the length of these lines can be determined, measurement 
points must be found, to which the measurement lines are drawn. 
To find these points, move out on the horizon from the point of dis- 
tance on the left, as far as it is from point of distance to a (point of 
station), and mark the point 7?i; and from the point of distance on 
the right, move out on the horizon as far as it is from the point of 



64 



Elements and Rules of Perspective. 



distance to a, and mark the point/, which is the measurement point 
for the line receding from a. 




Give an explanation of Figure 52. 



CHAPTER XIX. 

AN EASY METHOD FOR DRAWING A PERSPECTIVE WHEN THE 
PIvAN IS GIVEN (figure 53, PAGE 67). 

1. I^OCATE on the sheet of paper a vertical line (the Prime 
Vertical — P. V.). 

2. Draw the plan, abed, either in a proper position on the 
paper, at the desired angle to the P. V., so that the nearest corner or 
angle of the plan comes on the P. V. Or, draw the plan on a sepa- 
rate piece of paper, and adjust same on the P. V. to the best or most 
desirable angle for viewing the most prominent features of the 
structure. 

3. Locate the station point on the P. V., at a suitable distance 
from the nearest point of the plan (about four times the greatest 
dimension). . 

4. Locate a horizontal line (picture plane) on which all the 
measurements of the plan are projected by ruling lines to the station 
point from the features on the plan. 

Note. — This line ef determines the size of the perspective, and is to 
be located at any point between the nearest point of the plan {a) and the 
station point, according to the judgment of the draughtsman. The nearer 
to the station point, the smaller the perspective. 

5. Locate the base line. 

6. Locate the horizon. 

Ele. Pers.— 5. (65) 



66 KlyKMKNTS AND RUI.ES OF PKRSPECTIVK. 

7. I^ocate the vanishing points (V. P.) by projecting lines 
from the station point, parallel to ab and ac^ until they intersect 
the picture plane at o and m. Project vertical lines from these 
points of intersection, until they intersect the horizon. These latter 
intersections will form the vanishing points. 

8. At the left edge of the paper, draw the vertical measure- 
ment line (for vertical heights), projecting, some above and below 
the horizon indefinitely. (The prime vertical may be used to serve 
the purpose of this measurement line.) 

9. From b and c draw lines to the station point, intersecting 
the picture plane. Project these intersections, e and f, by vertical 
lines until they cross the horizon, prolonging indefinitely. (These 
lines establish the limits of the perspective.) 

10. lyay off on the measurement line the different vertical 
heights of the structure, with reference to their relative positions 
to the horizon. 

11. Project (horizontally) the points indicating the vertical 
heights over to the prime vertical. 

12. From these points draw straight lines toward the van- 
ishing points, outlining the foreshortened elevations. 

13. Locate all doors, windows, and other features of the plan, 
on the picture plane, as described in 9. 

14. Project, by vertical lines, to their relative positions in the 
perspective outline of the structure. 

15. Establish heights of the above features on the measure- 
ment line; project to the prime vertical, and vanish toward van- 
ishing points until these lines intersect the vertical (14). 

16. Proceed according to previous directions until the picture 
is completed. 



BiyEMENTS AND RuivES OF PERSPECTIVE. 



67 




Fig' 53* 



CHAPTER XX. 



ISOMBTRIC PROJKCTION. 



IsoMBTRic projection differs from perspective and orthographic 
projection, inasmuch as it shows the view of the entire object, and 
all the lines in the drawing may be measured by a uniform scale. 

It is called the perspective 
of the workshop. This 
style of representing ob- 
jects was first used by 
Professor Farish, of Cam- 
bridge, in 1820. 

In perspective drawings 
objects diminish in size as 
they appear more distant, 
according to laws of optics, 
and it is difficult to meas- 




Pig' 54- 



ure their sizes. In orthographic projection two drawings are re- 
quired, and the lengths of the lines are altered according to the 
angle at which the object may be placed. The whole system of 
isometric projection — meaning projections w4th equal measure- 
ments — is based on a cube so situated with relation to the hori- 
zontal plane that its projection on the vertical plane will be a 
hexagon bcdhfe (Fig. 54). The three visible faces of the cube are 
equal in the representation. The angles are not right angles, as in 

(68J 



El^EMENTS AND Rui.ES OF PERSPECTIVE. 



69 




^g. 55. 



the actual cube, but are acute and oblique — two acute angles of 
60°, and two oblique angles of 120°. 

The line ^c leaves the horizontal line mo at an angle of 30°, 
making the representation of the right angle an acute angle, a5c, 
measuring 60°. The lengths of the lines are established by a scale. 
Vertical hues are represented by vertical lines. The angle at a 
measures 120°. The 
line ad, and all other 
lines of the obj ect par- 
allel to dc, are made 
parallel to 5c in the 
representation. The 
faces ade/ and ad/if 
are drawn in the 
same manner as the 
face adcd. 

An isometric drawing unites plan, elevation, and projected 
view, in one. 

To construct an isometric scale so that the object to be drawn 
may be one-twelfth of the real size, proceed as follows: — as the 
scale is one inch to the foot, and as an inch is one-twelfth of a 
foot, each of the twelfths will represent an inch. 

Draw the line dd (Fig. 55) an inch and a half long, represent- 
ing the. real length of an object one foot and a half. Mark on 
dd the twelfths of inches which are to represent inches on the scale. 

Make the angle ddm 30°, with the set square, and bisect it. 
This gives the angle Mo, 15°. From the point d draw an angle 
of 45°. From each point marked off on the line draw lines 
parallel to the line dx. The divisions on dx will represent inches, 
and the line dx is an isometric scale of ^. Or, instead of making 
a scale, lay off on the lines which will represent the figure when 



70 El^EMKNTS AND Rui.KS OF PKRSP:eCTlVK. 

completed, in isometric projection, the exact measurements. Thus, 
to draw a cube of 4' o'' in isometric projection, lay off the line ab 
(Fig. 54) vertical, 4' o" long. From the point b project the lines 
be and be at angles of 30° each with the base line, measuring 4' o" 
along the lines to points e and e. At these points establish verti- 
cals 4' o" long. Connect the point a with f and d by lines par- 
allel to be and be. From d and f project lines parallel to af and 
ad, until they meet in h. Represent the bottom of the cube by 
dotted lines from e and c, parallel to fh and dh respectively. 



CHAPTER XXI. 

OBI^IQUE PKRSPKCTIVK. 

A LINK is in oblique perspective when it is not parallel to either 
the ground plane or the picture plane — when it is neither hori- 
zontal nor vertical, but slanting. These lines occur in the steeples 
of churches, gables of houses, uneven roads, covers of open boxes, 
books, etc. These oblique lines do not vanish on the horizon, as 
do the vanishing lines in parallel and angular perspective, but on 
a line perpendicular to the horizon. 

A line lying flat on the ground plane at the right or left of 
the observer, and at right angles to him, vanishes in the point of 
sight. If this line is inclined, that is, if one end is raised from the 
ground plane, the perspective inclination will not tend to the point 
of sight, but to a point above it in prolongation of the prime 
vertical (Fig. 57). The length of this oblique line is determined 
by a point on the prime vertical below the point of sight. 

A line lying flat on the surface at an angle of 45° to the 
picture plane, vanishes in the point of distance. If this line is in- 
clined, instead of vanishing in the point of distance, it will vanish 
in a point above the point of distance on a line perpendicular to the 
horizon at that point; and the oblique line will be measured by 
a point on this vertical line, prolonged below the point of distance 

(Fig. 56). 

If a line is at an angle of 60° to the picture plane, it vanishes 

in a point on the horizon between the point of sight and the point 

(71) 



72 ElyKMKNTS AND Rui.KS OF PERSPECTIVE;. 

of distance. If the end is elevated, the hne will not vanish in this 
vanishing point, but in a vertical line drawn through the vanish- 
ing point for 60°, and the length will be determined by a point 
on the same line below the vanishing point on the horizon. 

The vanishing point for an oblique line is always in a vertical 
above or below the point it would have vanished in, had it occupied 
a level position; and the measurement point for the oblique line 
is in the same vertical line. 

In parallel perspective all lines that vanish in the point of sight 
are measured by lines that vanish in the points of distance, and 
these points are measurement points for all lines that are fore- 
shortened in parallel perspective. 

If the vanishing point for an oblique line is in the prime verti- 
cal above the point of sight, it is found by means of an angle at 
the point of distance (the measuring point for all lines that vanish 
at the intersection of the prime vertical and horizon), the side of 
which is prolonged until it meets the prime vertical, and locates 
the vanishing point for the oblique line. 

The length of the oblique line is determined by a measure- 
ment point on the prime vertical as far from the vanishing point 
for the oblique line, as the distance from this vanishing point to 
the point of distance. 

The point P. P. is a vanishing point for an oblique line; the 
length of this oblique line is determined by the measuring point c. 

The point c is found by moving down on the prime vertical, the 
same line on which the vanishing point is located (Fig. 57), as far 
from the point P. P. , as it is from P. P. to P. S. , thus making the 
line P. P—c equal to the line P. P. —P. S. 

Note. — The vanishing points in oblique perspective are by some authors 
termed accidental points. 



Elements and Rules of Perspective. 



73 



^p.p 



p. p 




Pig. 56. 



Fig. 57* 



RUIvES 

GOVERNING THK lylNKS AND SURFACES OF OBJECTS IN 
OBI.IQUE PERSPECTIVE. 

RuiyK I. To find a vanishing point for an oblique line, con- 
struct an angle at the angular vieasurhig point equal to the angle 
made by the oblique line, and prolong the line forming the angle 
until it touches the perpendicular erected on the angular vanishing 
point; the point where these two lines meet is the vanishing point 
for the oblique line. 

RUI.E II. To find the measuring point for the oblique line, 
move from the oblique vanishing point on the vertical line, down- 
ward to a point as far from the vanishing point as the vanishing 
point is from the point where the angle was measured off. 

RuivE III. lyines parallel in the object vanish in one point 
in the drawing. 



(74) 



Elements and Rules of Perspective. 



75 




Figf 5S. 



CHAPTER XXII. 

KXPI^ANATION OF FIGURK 58. 

Probi^km. — Place in perspective a floor, 16 ft. x 10 ft., the 
nearest corner 5 feet to the left of the observer, receding at an 
angle of 45°; on this floor draw a trap door, 4 ft. x 5 ft., with 
the door one-fourth open. The nearest corner of the door is 2 
feet from the left side, and i foot from the right side of the floor. 

Draw the plan, and place the rectangular surface in perspec- 
tive, and mark it abed (Fig. 45). I^ocate the outlines of the door 
in the ground plan according to the problem, and mark them 1,2, 
3, 4. Prolong the lines from these points to the base line. I^ocate 
the measurement points on the base line, and from these draw 
lines to the points of distance, and where they cross, locate the 
points I, 2, 3, 4, in the perspective view. 

As the door is one-quarter open (according to Rule I) con- 
struct an angle of 45° at the point of sight, and prolong the side 
of this angle until it reaches a perpendicular over the point of dis- 
tance. At this point locate the vanishing point for the oblique 
lines; then to this vanishing point, draw lines from 2 and 3; to 
find the length of these lines it is necessary to find the measure- 
ment point. This point is on the vertical through the point of 
distance as far from the vanishing point for oblique lines as it is 
from this vanishing point to the point of sight (Rule II). If the 
door were half-way open its perspective height would be deter- 
mined by a 5 -foot vertical line m perspective, from the point 3; 
(76) 



Elements and Rules of Perspective. 77 

p.p. 




Pig' 59- 

a 5-foot line from this point terminates at the point e ; from this 
point to the measurement point draw a Hne. Where this Une crosses 



78 



Ki.KME;NTS and RUI.KS OF Perspkctivb. 




Pig. 60. 

the oblique line from 2, locate the point 5, and from this to the 
point of distance on the left, draw a line (Rule III) to represent 
the upper edge of the door. 



Elements and Rules of Perspective. 79 

Problem (Figure 59). — View of a rectangular box 8 ft. x 16 x 
II ft., surmounted by a triangle, with a base 8 ft. x 11 ft., and a 
vertical height of 3 feet. Nearest corner of box 11 feet on the 
right of the observer. 

Construct the ground plan according to Figure 45, and draw 
the rectangular box according to Figure 47. 

Find the vanishing and measurement points for oblique lines 
according to rules on page 74. 

Problem (Figure 60). — View of a 4 -foot cubical box, the 
cover one - fourth open. 

Construct the ground plan (Fig. 44), and draw the box ac- 
cording to Figure 47. 

Find the vanishing and measurement points for the cover 
according to rules on page 74. 



CHAPTER XXIII. 



PROBLEMS. 



1. Pi,ACK in perspective a 4- foot square, 6 feet to the left of 
the prime vertical line, and a 3^ -foot square, 5 feet to the right 
of the prime vertical line, both resting on the base line. 

2. Place in perspective a series (4), of 2-foot squares, 2 feet 
apart. The first resting on the base, the nearest corner 5 feet to 
the left of the prime vertical. 

3. Place in perspective a 3- foot cube, 2 feet back from the 
base line, 5 feet to the left of the prime vertical line. 

4. Place in perspective a box (resting on the base line) 7 feet 
high, 3 feet wide, and 2 feet deep, the nearest corner 7 feet to 
the left of the prime vertical; and one, 4 feet to the right of 
the prime vertical, 8 feet long, 4 feet high, and 4 feet wide, 2 feet 
back from the base line. 

5. Place in perspective a series of circles (2), 3 feet apart; the 
first on the base line, the diameter tangent to the base line, 6 feet 
to the left of the prime vertical. 

6. Place in perspective a cylinder, 4 feet in diameter; the axis 
of the cylinder 6 feet to the right of the prime vertical, the base 
of the cylinder tangent to the base line. 

7. Place in perspective an oval figure, 6 feet by 3 feet; the 
3 -foot diameter perpendicular to the base line, 9 feet from the 
prime vertical. 

8. Place in perspective a pyramid, with a 4-foot square base, 

(80) 



Elements and Rules of Perspective. 8i 

vertical height 7 feet, nearest corner 3 feet to the left of the prime 
vertical, front line of the base 2 feet back from the base line. 

9. Place in perspective a hexagon, one of the sides resting 
on the base line, 5 feet to the right of the prime vertical. 

10. Place in perspective a pyramid, with a hexagonal base, 
and an altitude of 9 feet vertical; direction 7 feet to the right of 
the prime vertical. 

11. Place in perspective a prism, 7 feet in altitude, with a 
base 4 feet wide by 6 feet long — front line resting on the base 
line. 

12. Place in perspective a skeleton cross — standard 9 feet 
high on a base 6 feet square, and i foot high. The nearest corner 
7 feet to the left of the observer, and 5 feet back from the base 
line. The cross is i ^ feet from the top of the cube, and is com- 
posed of I >^ -foot cubes. 

13. Place in perspective a cottage, 20 feet long, 10 feet wide, 
and 9 feet high, with a gable 5 feet high. 

14. Place in perspective a cottage, 30 feet long, 12 feet wide, 
and g% feet high, with a gable 5 feet high, and two windows 
and a door, each 3 feet wide, and 7 feet apart. 

15. Place in perspective a floor, 16 feet by 18 feet; the nearest 
corner 3 feet to the left of the observer, and 2 feet back from the 
base line. 

16. Place in perspective the interior of a room, 12 feet by 16 
feet, the point of sight in the middle of the back wall of the room; 
the front line of the floor on a level with the base; the height 
of the room 10 feet. 

17. Place in perspective a half circle (the diameter 4 feet), 3 
feet back from, and parallel to, the base; the nearest corner of the 
diameter 5 feet on the left of the observer. 

18. Place in perspective a half circle (the diameter 5 feet), 

Ele. Pers. — 6. 



82 KlvEMKNTS AND Rui.ES OF PERSPECTIVE. 

at right angles to the picture plane, 8 feet to the left of the ob- 
server; the nearest point 4 feet back from the base. 

19. Place in perspective a circle, vertical diameter 4 feet, at 
right angles to the ground plane, at a point 6 feet back from the 
base, and 7 feet on the right of the observer. 

20. Place in perspective a 6-foot square, 4 feet above, and 3 
feet to the right of the point of sight, and parallel with the ground 
plane. 

21. Place in perspective, 6 feet above the level of the eye, 
and 5 feet to the right of the observer, a circle 7 feet in diameter. 

22. Place in perspective a pyramid, 7 feet high — hexagonal 
base (six sides); the diameter, 5 feet, touches the base at right 
angles to it, at a point 11^ feet from the prime vertical. 

23. Make perspective drawing, plan, and elevations of a 3-foot 
cubical box situated on the ground plane 4 feet to the left of the 
observer, the front face of the box lying in the picture plane. 

24. Find a point on the ground plane 2 feet to the right of 
the observer and 5 feet back from the picture plane, 3 feet above 
the ground. 

PlyACE IN PERSPECTIVE THE FOI^IyOWING: 

25. A line 4 feet long at right angles to the picture plane, and 
situated 6 feet to the right of the observer, with one end in the 
picture plane 7 feet above the ground. 

26. A prism, having a base i foot square and an altitude of 
3 feet, situated 2 feet to the left of the observer and 3 feet back 
from the picture plane. 

27. A box 2 feet high, with base 6 feet by 3 feet, situated 
3 feet to the right of the observer and i foot back from the picture 
plane — the longest side to be parallel to the picture plane. 

28. A rectangular pyramid, base 2 feet square, altitude 4 



KlyKMKNTS AND RuivKS OF PERSPECTIVE. 83 

feet, situated 2 feet to the right of the observer, and touching the 
picture plane. 

29. A triangular pyramid, whose base is an equilateral triangle 
with sides of 3 feet, situated like No. 6. 

30. A circle 5 feet in diameter, lying 6 feet to the left of the 
observer, and touching the picture plane. 

31. A hexagon inscribed in above circle. 

32. A cone, with a base 2 feet in diameter and 3 feet high, 
and situated 8 feet to the right of the observer, and touching the 
picture plane. 

33. A horizontal line 5 feet long, lying on the ground plane 
at an angle of 45° to the picture plane, one end being in the picture 
plane and 4 feet to the right of the observer. 

34. A 3-foot square lying on the ground plane side, at an angle 
of 30° to the picture plane, touching the base 2 feet to the left of 
the observer. 

35. Inscribe an octagon in the above square. 

36. A hexagonal prism, each side of whose base is i foot, 
and whose altitude is 6 feet, situated 4 feet to the right of the 
observer, and 2 feet back from the picture plane. 

37. A cylinder 4 feet in diameter and 10 feet high, situated 3 
feet to the left of the observer and 6 feet back from the picture 
plane. Draw plan and elevations. 

38. A vertical plane 10 feet square, one side of which is in 
the picture plane, and which extends back at right angles to the 
picture plane, situated 12 feet to the right of the observer. 

39. Inscribe a circle in above plane. 

40. Inscribe a hexagon in above circle. 

41. A 3-foot cubical box with the lid one-quarter open (hinge 
edge toward picture plane), situated 4 feet to the right of the 
observer and 2 feet back from the picture plane. 



84 KlvKMKNTS AND Rui.ES OF PERSPECTIVE. 

42. A 3-foot cube, one face in ground plane, and the vertical 
faces to be at angles of 60° and 30° with picture plane, the angle 
nearest the spectator to be i foot to his right and 2 feet back from 
the picture plane. 

43. A right cone, 4 feet in diameter and 6 feet high, standing 
on the ground plane and touching the picture plane 2 feet on the 
right of the spectator. 

44. A hexagonal pyramid, of which the sides of the base are 2 
feet and the height 6 feet, standing on its base on the ground plane; 
the center of the base is 3 feet back from the picture plane and i 
foot to the left of the spectator. 

45. A prism, whose base is an equilateral triangle, each side 5 
feet, its height being 8 feet, with one side lying on the ground plane, 
its long edges being inclined at 60° to the picture plane, toward the 
right, and the angle nearest the spectator being 3 feet on his left 
and 2 feet from the picture plane. 

46. A base-ball diamond (a square, 90 feet on a side), inclined 
40° to the plane of the picture. 

47. Find a point 2 feet to the left of the observer and 2 feet 
back from the picture plane; and another 5 feet to the left of 
observer and 7 feet back from the picture plane. Join these two 
points {a and b) and find the real distance from a to b. 

48. A truncated cone, the lower base 2 feet in diameter, the 
upper base i foot in diameter, and its altitude 3 feet. 

49. Surmount the above truncated cone with a cone whose base 
coincides with the upper base of the truncated cone, and whose alti- 
tude is I foot. 

50. A 6- foot vertical square, standing at an angle of 60° to the 
picture plane, the nearest vertical side being 4 feet back from the 
picture plane. 

51. Inscribe a circle in a square. 



EI.EMENTS AND RULES OF PERSPECTIVE. 85 

52. Inscribe a hexagon in a circle. 

53. I^ocate a point in perspective, 3 feet to the left of the 
observer, and 2 feet back from the base line. 

54. I^ocate a point in perspective, 5 feet to the right of the 
observer, and 3 feet back of the base line. 

DRAW IN PERSPECTIVE THE FOIvI^OWING: 

55. A 3-foot vertical line, 4 feet to the left of the observer, 
and 2^ feet back of the base line. 

56. A 7-foot vertical line, 5 feet to the right of the observer 
and 2 feet back of the base line. 

57. A 3-foot square, 5 feet to the left of the observer, the 
front side touching the base line. 

58. A 4- foot square, 4 feet to the right of the observer, and 2 
feet back of the base line. Draw its diagonals and its diameters. 

59. Three rectangles, 4 feet long and 2 feet wide, one directly 
in front of the observer, one 5 feet to the left (nearest corner), and 
the other 5 feet to the right — front sides touching base line. 

60. A 4-foot cube, the front edge resting on the base line 2 
feet to the left of the observer. 

61. An 8- foot cube, 4 feet to the right of the observer, the 
front edge touching the base line. 

62. Three 6-foot cubes, faces parallel to picture plane, one di- 
rectly in front of the observer, one 5 feet to the left (nearest cor- 
ner), and the other 7 feet to the right, the front edges touching 
the base line. 

63. Three 6-foot cubes, one directly in front, one 5 feet to the 
left, the other 5 feet to the right; the front line of each 2 feet 
back of base line, and front faces parallel to picture plane. 

64. A rectangular box 7 feet long, 3 feet high, 4 feet wide, 



86 KlKMKNTS and RUI.KS OF Pkrspkctive. 

and 5 feet to the left of the observer; front edge on the base 
line. 

65. A rectangular box 8 feet high, 4 feet square at base, 6 
feet to the right of the observer, and 2 feet back of base line. 

66. Three rectangular boxes 8 feet high, 3 feet square at base; 
one directly in front, one 4 feet to the right, and the other 4 feet 
to the left of the prime vertical. 

67. A table 5 feet long, 3 feet high, 2^ feet wide; 4 feet to 
the left of the observer. 

68. A row of poles 15 feet high at right angles to ground 
plane, and 8 feet apart; nearest pole 6 feet to right or left of the 
observer. 

69. Hitching posts, three on each side of the prime vertical, 
poles at right angles to ground plane 2>% f^^t high and 5 feet 
apart. 

70. A view of a street running at right angles to the picture 
plane and crossed by one running parallel to the picture plane. Draw 
pavement 3 feet wide on each side of street, and fences, poles 3^ 
feet high, 3 inches wide, and ^ foot apart. Street 20 feet wide. 

71. Draw lines indicating perspective of street; single car track 
and electric poles on either side, poles 15 feet high and 20 feet apart, 
observer equally distant from either side. 

72. Three telegraph poles 15 feet high and three lamp-posts 8 
feet high, alternating telegraph and lamp-posts 10 feet apart, poles 
parallel to picture plane and at right angles to ground plane. 

73. Poles 10 feet high at right angles to ground, parallel to 
picture plane 6 feet apart, nearest poles on either side of the observer 
4 feet. 

74. Lamp-posts 10 feet apart, 8 feet high, posts parallel to pic- 
ture plane, line of posts at right angles to picture plane, round 
globes, etc. 



Elements and Ruizes of Perspective. 87 

75. An iron fence and gate entrance, fence 3 feet high, single 
rod and gate 4 feet by 3 feet, finish as pupil or teacher suggests. 

76. A room 20 feet long, 16 feet wide, 10 feet high, with win- 
dows 6 feet high, 4 feet wide, 4 feet apart, 2^ feet above floor. 
Windows in rear wall, floor i foot planks, middle of rear wall 
directly in front of observer. Place doors 7 feet high, 4 feet wide, 
in center of each side wall. 

77. A circle, radius 4 feet, lying flat on ground plane, diameter 
at right angles to base line, 10 feet to the right of the observer. 

78. A cone 8 feet to the left of the observer, diameter of base 
6 feet, altitude 3 feet tangent to base line. 

79. A cylinder, diameter i foot, perpendicular height 8 feet, 
situated 6 feet to the left, circumference touching base line. 

80. An arch passage way perpendicular to ground plane, 10 
feet high to arch, radius of arch 3 feet. 

81. A pyramid that has for its base a square. Pyramid 7 feet 
to the right of the observer, front edge 2 feet back of base, perpen- 
dicular height 6 feet, base 4 feet square. 

82. A monument, base 8 feet square and i foot high, 8 feet to 
the right of the observer, front edge touching base line, pyramid top 
directly over center of base, perpendicular height 10 feet to top 
square which is 2 feet. Place corners of the pyramid i foot from 
centers of the square base, front face parallel to picture plane (scale 
^ inch to foot). 

83. An ice chest 3 ft. long, 3 feet wide, 3 feet high, to the left • 
of observer; 2 feet back of base line; front face parallel to picture 
plane; panel front and sides. 

84. A pyramid with a base 9 feet square, and an altitude of 12 
feet, the nearest corner being 6 feet to the left of the observer and 
3>^ feet back from the picture plane. 

85. Three two-foot cubical boxes, lying in a straight line 



88 ElvKMENTS AND Rui.ES OF PERSPECTIVE. 

parallel to, and 6 feet back from, the perspective plane, and to the 
right of the observer; the nearest edge of the nearest box being 
directly in front of the observer and the boxes being separated from 
each other by a space of 6 inches. 

86. A rectangular box, 12 feet long, 3 feet wide, and 3 feet 
high, the nearCvSt corner located in the base line 2 feet to the right 
of the observer; the box receding lengthwise toward the right, at 
an angle of 30°. 

87. A box 7 feet high, with a base 3 feet square, 8 feet back 
from the base line, and 10 feet to the right of the observer, 
and a 2 ft. cube resting on the ground plane and the nearest corner 
lying 2 feet to the left of the observer and 4 feet back from the 
picture plane. 

88. A stool, circular top, diameter of circle i foot, legs 2j^ 
feet high, stool situated to right of observer 3 feet and back of base 
line 2 feet. 

89. A chair, seat i }^ feet square, legs i ^ feet long, back 2 feet 
high, situated to left of observer 5% feet, 2 feet back of base line, 
and the side of chair parallel to picture plane. 

90. A chair, seat 2 feet square, legs i^ feet long, back 2^ 
feet high, situated to right of observer 5 feet, and front of chair 
facing observer parallel to picture plane. 

91. A bench 3 feet long, i ^ feet high and i foot wide; to right 
2- foot bench resting on base line (scale >^ inch to i foot). 

92. A table 2j^ feet high, 2 feet wide, 5 feet long, situated to 
right of observer 3 feet, drawer in center of front of table 1 5^ feet 
long, ^ foot wide, front face parallel to picture plane and back of 
base line 2 feet. 

93. A trunk 3 feet long, 2 feet wide, 2 feet high, 2 feet to left; 
handles and straps on base line parallel to picture plane (scale ^ 
inch to I foot). 



Elements and Rules op Perspective. 89 

94. A 3-foot cube, front edge resting on the base line, 5^ feet 
to the left of the prime vertical. 

95. A 4-foot cube, 5 feet to^ the right of front edge, 3>^ feet 
back of base line. 

96. Two 3-foot cubes, the front edge of one resting on the base 
line. The front edge of the other to be 5 feet back of the base line 
(two feet from first cube), both cubes being 5 feet to the left of the 
prime vertical. 

97. A box 7 feet long, 4 feet wide, and 4 feet high, so placed 
that the square ends are parallel to the picture plane. Front edge 
to rest on base line, nearest corner 5 feet to the right of the prime 
vertical. To the right of this box and adjoining it, construct a 
square-based pyramid. Base 4 feet square, altitude 7 feet, front 
edge resting on base line. 

98. A wardrobe 9 feet high, 6 feet long, and 2 feet wide, in 
corner of room; back of base line 3 feet; to left of observer 6 feet;^ 
finish as desired. 

99. A circle 8 feet in diameter, lying flat on the ground; the 
diameter at right angles to base line, and 7 feet to the left of the 
prime vertical. 

100. A circle 10 feet in diameter standing upright, perpen- 
dicular to the picture plane, at a distance of 8 feet to the right of 
the prime vertical. 

loi. A 6-foot square, 7 feet to the left of the observer, the 
corner resting on the base line and the nearest side receding from 
the picture plane at an angle of 45°. 

102. A rectangle 5 feet by 2 feet; the nearest corner 7 feet to 
the right of the observer and in the base line; the nearest long side 
receding toward the left, at an angle of 45° from the picture plane. 

103. A 9-foot square, 2 feet to the left of the observer and 5 
feet back from the base line, at an angle of 45°. 



90 KlyKMKNTS AND RULKS OF PERSPKCTIVK. 

104. A rectangular box, 12 feet long, 3 feet wide, 3 feet high; 
the nearest corner located in the base line 2 feet to the right of the 
observer; the box receding (lengthwise) toward the right, at an 
angle of 30°. 

105. A box 7 feet high with a base 3 feet square; 8 feet back 
from the base line, and 2 feet to the left of the prime vertical, at an 
angle of 70°. 

106. A tesselated floor, 20 feet wide and 30 feet long, divided 
into 2-foot squares, the nearest corner lying in the base line 7 feet 
to the right of the observer and receding (lengthwise) toward the 
right, at an angle of 50°. 

107. A pyramid 12 feet high, having for its base a 4- foot 
square, having its nearest corner in the base line, and 3 feet to the 
right of the observer, and inclined 45° to the picture plane. 

108. A triangular prism 10 feet high, the base being a right- 
angled triangle with a base and perpendicular of 3 feet, the nearest 
angle lying 3 feet to the right of the observer and 4 feet back from 
the picture plane; the hypotenuse receding toward the right at an 
angle of 65° with the picture plane. 

109. A piece of stovepipe 3 feet long and 6 inches in diameter, 
its nearest point lying in the picture plane and 3 feet to the right of 
the observer, the pipe receding toward the right, at an angle of 40°. 

no. A circle 10 feet in diameter, inscribed in a vertical square, 
the nearest side of which is in the picture plane and 4 feet to the 
right of the observer, and receding toward the left at an angle of 60°. 

111. Three 2-foot cubical boxes, lying in a straight line parallel 
to and 6 feet back from the picture plane; and to the right of the 
observer, the nearest edge of the nearest box being directly in front 
of the observer, the boxes being separated from each other by a 
space of 6 inches. 

112. A pyramid with a base 9 feet square, and an altitude of 



ElvEMKNTS AND RuivKS OF PERSPECTIVE. 9 1 

12 feet, the nearest corner being 6 feet to the left of the observer 
and 3^ feet back from the picture plane. 

113. A post I foot square and 12 feet long, lying on the 
ground plane, extending toward the right, and running back, at 
an angle of 30° with the picture plane; the nearest corner of the 
post being 2 feet to the left of the observer and 2 feet back from 
the picture plane. 

114. An octagon inscribed in a 9-foot square, — the square 
lying on the ground plane, inclined 45° to the picture plane, the 
nearest corner being 2 feet to the left of the observer and 6 feet 
back from the picture plane. 

115. A tesselated pavement 10 feet square, divided into i-foot 
squares; lying on the ground plane, inclined back tow^ard the right 
at an angle of 20° with the picture plane, the nearest corner lying 
6 feet to the left of the observer, and in the base line. 

116. A board fence, running back at right angles to the picture 
plane, on level ground, and the nearest end lying in the picture 
plane, 10 feet to the right of the observer, the fence to be designed 
or selected by the pupil. 

117. Draw isometric projections of: 
(i.) Hollow cube. 

(2.) Rectangular box. 

(3.) Flight of four steps. 

(4.) Newel post. 

(5.) Hollow cylinder. 

(6.) Section of a porch railing. 

(7.) Brick chimney. 

(8.) Wash bench. 

118. A view of a 9-foot cube inclined 45° to the ground plane, 
and surmounted by a wedge-shaped solid with a base 9 feet square. 



92 EI.KMENTS AND Rui.KS OF PKRSPKCTIVK. 

and an altitude of five feet, the nearest corner of the cube being in 
the base line lo feet to the left of the observer. 

119. A pyramid, with an altitude of 7^ feet, and a base 3 feet 
square, the nearest corner being i foot to the right of the observer 
and I foot back from the picture plane; the pyramid receding 
toward the right at an angle of 30° with the picture plane, and 
upward at an angle of 15° with the ground plane. 

120. A prism, with an altitude of 10 feet, and having for 
its base a 5 -foot square, the nearest corner of which is 3 feet to 
the right of the observer and 2 feet back from the picture plane; 
the base receding toward the left at an angle of 60° with the 
picture plane, and upward at an angle of 20° with the ground 
plane. 

121. A 4-foot cubical box, inclined 45° to the picture plane, 
its nearest corner located in the base line 4 feet to the right of the 
observer; the lid of the box opened upward toward the right at an 
angle of 45°. 

k 

122. A floor, 15 feet by 12 feet, the nearest corner 4 feet to 
the left of the observer, receding at an angle of 45°. On this floor 
draw a trap-door 4 feet by 5 feet, with the door one- fourth open. 
The nearest corner of the door is 2 feet from the left side, and i 
foot from the right side of the floor. 

123. A view of a 9-foot cube, inclined 45° to the ground plane, 
and surmounted by a wedge-shaped solid with a base 9 feet square 
and an altitude of 5 feet, the nearest corner of the cube being in the 
base line, 10 feet to the left of the observer. 

124. A rectangular box, with a base 2 feet square and an alti- 
tude of 3 feet, surmounted by a pyramid with a base 2 feet square 
and an altitude of 2 feet, the box being inclined 45° to the picture 
plane, and inclined upward as it recedes toward the right, at an 
angle of 10° with the ground plane. 



ElvEMENTS AND RULES OF PERSPECTIVE. 



93 



125. A pyramid, with an altitude of 7^ feet and a base of 3 
feet square, the nearest corner being i foot to the right of the 
observer and 4 feet back from the picture plane, the pyramid reced- 
ing toward the right at an angle of 30° with the picture plane, and 
upward at an angle of 15° with the ground plane. 

126. A row of vertical posts, each i foot square and 7 feet 
high, receding to the right at an angle of 40° with the picture 
plane, and up a straight hill at an angle of 20° with the ground 
plane; the posts being 6 in number and 10 feet apart, the nearest 
corner of the nearest post being in the picture plane directly oppo- 
site the observ^er. 

127. Draw an isometric projection of : 

(i.) Watering trough, 10 feet by 2 feet base, i foot high 
(outside), and composed of boards 2 inches thick. 



(2 


) Anvil. 


(3 


) Wagon bed. 


(4 


) Carpenter's plane. 


(5 


) Hot-bed, showing glass covering. 


(6 


) Bench. 


(7 


) Grindstone. 


(8 


.) Cord of Wood (4 feet by 4 feet by 8 feet). 


(9 


) Flight of steps. 


(10 


) Ice chest. 


(II 


) Office safe. 


(12 


) Stove. 


(13 


) Chair. 


(14 


) Small stone bridge. 


(15 


) Railroad signal tower. 


128 


. A rectangular box, 12 feet long, 3 feet wide, and 3 feet 


high; tl 


le nearest comer located in the base line 2 feet to the right 



94 Klkmknts and RUI.KS OF Pkrspkctivk. 

of the observer, the box receding (lengthwise) toward the right, at 
an angle of 30°. I^id half way open. 

129. A colonial clock, 7 feet high, the base 2 feet square, 8 feet 
back from the base line, the nearest corner 5 feet to the left of the 
observer. 

130. A 4- foot square and inclined toward the left at an angle of 
45° with the ground plane, directly opposite the observer, and 5 feet 
back from the picture plane. In this square inscribe a circle. 

131. In the above circle inscribe a hexagon, and upon this 
hexagon as a base, construct a pyramid with an altitude of 8 feet. 

132. A pyramid 12 feet high, having for its base a 4 -foot 
square, having its nearest corner on the base line and 3 feet to the 
right of the observer, and inclined 45° to the picture plane. 

133. Draw in perspective a triangular prism 13 feet high, the 
base being a right-angled triangle, with a base and perpendicular of 
3 feet; the nearest angle lying 3 feet to the right of the observer, 
and 4 feet back from the picture plane; the hypotenuse toward the 
right at an angle of 65° with the picture plane. 

134. A piece of stovepipe 5 feet long and 6 inches in diameter; 
its nearest point lying in the picture plane and 3 feet to the right 
of the observer, the pipe receding toward the right at an angle 
of 40°. 

135. A board fence, running back at right angles to the picture 
plane, on level ground, and the nearest end lying in the picture 
plane, 13 feet to the right of the observer, the fence to be designed 
or selected by the pupil. 

136. A circle 10 feet in diameter inscribed in a vertical square, 
the nearest side of which is in the picture plane and 1 1 feet to the 
right of the observer, and receding toward the left at an angle of 60°. 

137. A box 3 feet wide, 10 feet long, and 4 feet high, the 
nearest lower corner of which is on the ground plane 5 feet to the 



Elements and Rules of Perspective. 95 

left of the observer and 4 feet back from the picture plane, the box 
receding toward the right at an angle of 25° with the picture plane 
and upward at an angle of 30° with the ground plane. 

138. A prism with an altitude of 15 feet, and having for its 
base a 5-foot square, the nearest corner of which is 3 feet to the 
right of the observer and 2 feet back from the picture plane, the 
base receding toward the left at an angle of 60° with the picture 
plane and upward at an angle of 20° with the ground plane. 

139. A 4-foot cubical box inclined 45° to the picture plane; 
its nearest corner in the base line 7 feet to the right of the observer; 
the lid of the box opened upward toward the right at an angle of 45°. 

140. A floor 15 feet by 14 feet, the nearest corner 4 feet to the 
left of the observer, receding at an angle of 45°. On this floor 
draw a trap-door 4 feet by 5 feet, with the door one-fourth open. 
The nearest corner of the door is 12 feet from the left side, and 
I foot from the right side of the floor. 

141. A view of a 12-foot square, inclined 45° to the picture. 

142. A 4- foot square, inclined 45° to the picture plane, and 
inclined upw^ard toward the left at an angle of 45° with the ground 
plane, the nearest corner being on the ground plane directly oppo- 
site the observer and 5 feet back from the picture plane. In this 
square inscribe a circle. 

143. A tesselated floor, 20 feet wide and 50 feet long, divided 
into 2-foot squares — the nearest corner lying in the base line 7 feet 
to the right of the observer, and receding (lengthwise) toward the 
right, at an angle of 50°. 

144. A 4-foot cube at 30° and 60° to the picture plane, one 
corner touching the base line 4 feet to the left of the prime vertical. 

145. A box 2>^ feet high, 5 feet long, and 2 feet wide, at 45° 
to the vertical plane, one corner touching the base line 5 feet to the 
right of the prime vertical. 



96 ElvKMBN^S AND RULKS OF PERSPECTIVE. 

146. A pyramid, the base a 5-foot square, altitude 8 feet, edges 
of base at an angle of 35° and 55° to picture plane, front corner 
being 6 feet from the prime vertical and 4 feet from the base line. 

147.' A tesselated pavement 30 feet square, blocks to lie square, 
and at an angle of 45° to the base line. 

148. A section of wall 24 feet long, parallel with base line; 5 
feet from line of direction and 3 feet back, 3 feet thick, 12 feet high, 
containing three arches 4 feet wide, and 9 feet to top of arches. 

149. An ice chest whose base is 3 feet square and 4 feet high, 
lying upon one of its sides; the nearest angle being 4 feet on the 
left of the spectator and 4 feet from the picture plane, and the long 
sides receding at an angle of 60° with the ground line. 

150. A cigar box in angular perspective at 45° to picture plane, 
the box 5 feet long, 3 feet wide, i foot high; to left — lid one-half 
open. ( Yt, inch to i foot scale. ) 

151. Two arched windows. Windows in wall 15 feet long — 
distance between windows 4 feet. Windows 4 feet wide and 8 feet 
long at highest point of arch. 

152. A piano, square grand, 4 feet high, 7 feet long, body i 
foot deep, 3 feet wide. Place pedals in center and legs 3 feet long 
(scale ^ inch to i foot); to left of observer 5 feet, at an angle of 45° 
to the picture plane. 

153. A street scene. A street 20 feet wide, side-walks 2 feet. 
Car track, lamp, and telegraph poles 10 feet apart, at right angle to 
the ground; houses as designed by pupil, on each side of street, 
observer standing directly in center of street. 

154. Tunnel in stone bridge, bridge wall 20 feet long; 12 feet 
high. Arch opening 8 feet, track with ties running into tunnels. 
Electric light pole with arm and lamp at entrance, observer directly 
in front of scene. 



SEP 16 Iby« 



